NSTSE Sample Paper Class 11 PCM

Class : 11_PCM Mathematics
1. Which of the following is an empty set ?
(A) {x|x is a real number and x2 – 1 = 0}
(B) {x|x is a real number and x2 + 1 = 0}
(C) {x|x is a real number and x2 – 9 = 0}
(D) {x|x is a real number and x2 = x + 2}
2. Find the sum to n terms of the series given below.
13 13 + 23 13 + 23 + 33
+ + +..........
1 1+3 1+3+5
3 n(2n2 + 9n + 13)
(A) n(n + 1) (n + 2) (B)
24 24
4n2 + 1 1 2
(C) 5 (D) 8 n 2n + 15
3. Which of the following is true about the graph of the
inequations x > 0, y > 0, 3x + 4y < 12 ?
(A) Exterior of a triangle.
(B) Interior of a triangle including the points on the sides.
(C) In the second quadrant.
(D) Does not exist.
4. A person appears for an examination in which there
are four papers with a maximum of m marks from
each paper. Find the number of ways in which one
can get 2m marks.
1
(A) 2m + 3 C3 (B) (m + 1) (2 m2 + 4 m + 1)
3
1
(C) (m + 1) (2 m2 + 4 m + 3) (D) 2m + 3
3
1

5. Let "Z" denote a complex number and define
1
S= :|Z|= 1 and Z 1 . Which of the following
1-Z
best describes the set "S", when "S" is interpreted
geometrically as a set of points in the complex plane ?
(A) S is a straight line parallel to the imaginary axis
(B) S is a parabola
(C) S is a circle
(D) S is a hyperbola

2

Class : 11_PCM Physics

6. An iron ball is dropped into a long jar containing
castor oil. How will it move ?
(A) It will fall with a constant acceleration equal to that
of gravity.
(B) It will fall with an acceleration slightly less than that
due to gravity.
(C) It will ultimately acquire a constant velocity.
(D) It will float in the oil.
7. A soap bubble assumes a spherical shape. Which of
the following statements is wrong ?
(A) The soap film tends to shrink to as small surface area
as possible.
(B) The soap film consists of two surface layers.
(C) Pressure of air enclosed by the soap film is same as
that of the atmosphere outside.
(D) Pressure of air enclosed by the soap film is more than
the atmospheric pressure.
8. A ball hits the floor and rebounds after an inelastic
collision. What happens in this case ?
(A) The momentum of the ball just after the collision is
the same as that just before the collision.
(B) The mechanical energy of the ball remains the same
in the collision.
(C) The total momentum of the ball and the earth is
conserved.
(D) The total energy of the ball and the earth is conserved.
3

9. Viscous force is somewhat like friction as it opposes
the motion and is non-conservative but not exactly
so, Why ?
(A) It is velocity dependent while friction is not.
(B) It’s velocity decreases and becomes zero.
(C) It is temperature independent while friction is not.
(D) It is independent of area like surface tension while
friction depends on the area of contact.
10. If for a liquid in a vessel force of cohesion is twice of
adhesion, then which of the following is not true ?
(A) The meniscus will be convex.
(B) The liquid will wet the solid.
(C) The angle of contact will be obtuse.
(D) There will be capillary descent.

4

Class : 11_PCM Chemistry
11. Which of the following can be used to prepare a
buffer solution ?

(I) From a mixture of sodium acetate and acetic acid
in water.
(II) From a mixture of sodium acetate and hydrochloric
acid in water.
(III) From a mixture of ammonia and ammonium
chloride in water.

(A) (I) and (II) only (B) (II) and (III) only
(C) (I) and (III) only (D) (I), (II) and (III)
12. For the reaction. 2Cl–(g) Cl2(g) + 2e–. What are the
signs of  H and  S ?
(A)  H - Negative;  S - Positive
(B)  H - Negative;  S - Negative
(C)  H - Positive;  S - Negative
(D)  H - Positive;  S - Positive
13. What is the purpose of exhaust system in limekilns
where the decomposition of limestone takes place ?
(A) To drive away, CO2 gas and make the reaction proceed
for completion.
(B) To reduce the temperature of the reaction.
(C) To make the reaction attain equilibrium in less time.
(D) All of the above

5

14. Why can H2S in presence of dilute HCl precipitate out
only second group radicals but not fourth group
radicals ?
(A) HCl activates H2S.
(B) HCl decreases concentration of sulphide ions.
(C) HCl increases concentration of sulphide ions.
(D) Sulphides of IV group are unstable in HCl.
15. Which of the following electronic configurations
represents the violation of both Aufbau principle and
Hund’s rule ?

(A)
3s 3p 3d 4s

(B)
3s 3p 3d

(C)
3s 3p 3d

(D)
3s 3p 3d 4s

6

Class : 11_PCM Critical Thinking
16. The hidden figure in block 10 is ______.

(A) (B) (C) (D)

17. Count the number of blocks in the given figure.

(A) 105 (B) 98 (C) 102 (D) 100
18. Identify the 3-dimensional object from the given three
views.

(A) (B) (C) (D)

7

19. Arrange the following words in a logical sequence.
(1) Never (2) Sometimes
(3) Generally (4) Seldom
(5) Always
(A) 3, 5, 1, 4, 2 (B) 3, 5, 4, 2, 1
(C) 5, 3, 1, 2, 4 (D) 5, 3, 4, 1, 2
20. Pick the TWO answer choices that will come together
to make the figure shown. Pieces may be reflected
and/or rotated.

8